The study is devoted to the concept of data mining formulated in the setting of fuzzy sets. It is shown that the essence of revealing relationships within the data sets lies in context dependent search being formulated by the user. Some crucial links between data mining and fuzzy modelling are identified. Numerical experiments are also provided.
The paper deals with the notion of fuzzy systems described by means or fuzzy relational equations with triangular norms. Some fundamental pro Menu concerned with identification and control arc formulated and several algorithms are provided. An applicability of a concept of fuzzy discretization in system analysis is pointed out. Numerical results obtained form an illustration of theoretical background considered.
With the development of different kinds of techniques, especially the Internet of Things (IoT), a large amount of quantitative (either numeric or categorical) data have been generated, transmitted, and stored in the modern society. People hope to understand the interested phenomenon from the collected quantitative data by utilizing different data analysis methods. Exploring the structure of data (e.g., the cluster centers or prototypes) has always been a hot spot in the domain of data mining and knowledge discovery, yet it seems that the modeling and analyzing process still focus on a low-level abstraction of the data because normally, the structure found is only represented by some numeric data points. In this study, we highlight that a low-level abstraction may not be a user-friendly way for people to grasp the knowledge contained in the data. Instead, we explore the structure of the data from a perspective of symbolic analysis. Specifically, two modes of abstraction are proposed. In the vertical mode (i.e., values of each feature are abstracted), the numeric prototypes are characterized by the symbolic prototypes such that people could get rid of being stuck in minor details of each feature. In the horizontal mode (i.e., values of each prototype are abstracted), the linguistic summarization is used to describe all the features of each symbolic prototype such that people could immediately grasp the essential information conveyed in the symbolic prototype. We conduct comprehensive experimental studies on the publicly available data to illustrate the feasibility and validity of the proposed symbolic analysis process.
An unconventional interpretation of Kohonen self-organizing maps is presented. It employs linguistic variables and mechanisms of fuzzy decision theory to quantitatively reveal pattern structure in the map following self-organization. A simple example of pattern clustering is provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Component analysis is a common method used for the interpretation of data; however, in the case of pattern classification, the transformation of possibly correlated features into a new set of uncorrelated variables, must be used with caution since a principal component, which may account for significant variance in the data, is not necessarily discriminatory. To compensate for this deficiency, we present a classification method using an adaptive network of fuzzy logic connectives to select the most discriminatory principal components. We empirically evaluate the effectiveness of this classification method using a suite of biomedical datasets and comparing its performance against a set of benchmark classifiers.
The author introduces a method for dealing with imprecise objectives involved in the process of decision-making. A three-stage form of the system is proposed. It comprises three basic functional components realizing matching, nonlinear transformation, and inverse matching. The proposed scheme has a referential structure which shows that the fuzzy set of a decision is not determined by the objectives themselves, but by the levels of the matching with some prototype decision situations. Both matching and inverse matching procedures involve some logic-based mechanisms (equality indices). Neural nets are used to realize the nonlinear mapping indicated in the general scheme. Several advantages of the referential model, including exhaustive usage of knowledge about the decision problem conveyed by prototype situations, and an introduction of mechanisms of evaluation of the relevancy of fuzzy decisions, are highlighted. Additional indices expressing consistency of decision scenarios are developed. Detailed numerical studies demonstrate the performance of the method and provide some additional background concerning an evaluation of the results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Generally, fuzzy models, especially rule-based models, are designed in a monolithic manner, meaning that all data are used <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">en bloc</i> to design the model. At the same time, there is a visible need to cope with the ever-increasing volumes of data (both in terms of the number of data and their dimensionality) as well as being faced with distributed data located at various locations. The objective of this article is to develop a concept and provide a design framework as well as assess its performance for constructing a collection of rule-based models on a basis of a randomly sampled repository of data and then realize their aggregation. More specifically, for the sampled data, the design of each model is carried out in a standard way as commonly encountered in the case of Takagi–Sugeno (TS) rule-based models and next augmented by gradient boosting. The aggregation is realized by optimizing a weighting scheme applied to the results of the individual models. Our intent is also to carefully demonstrate the performance offered by the mechanisms of machine learning applied in the setting of rule-based models, which is an original task completed before. A number of high-dimensional data are used in the experimental studies to complete a thorough assessment. A comparative performance analysis is reported with respect to the monolithically developed TS models.
Considering the conditions that: 1) same linguistic term means different things for different people; 2) flexible semantics cannot be represented by original linguistic term; and 3) some semantics given by decision makers are possible to be changed during the consistency improving process, we bring some flexibility and personality into hesitant fuzzy linguistic preference matrix structures by allowing the linguistic preference matrices to be granular rather than numeric, providing a new characterization of linguistic preference matrices. Inspired by the thought of granular computing, this article proposes a new hesitant fuzzy linguistic method to deal with issues when a lot of decision makers provide hesitant and uncertain preference information in the decision-making process. First, we design a multiplicative consistency index and calculate its thresholds corresponding to different dimensions of preference matrix by the Monte Carlo experiment. Then, we construct a hesitant fuzzy linguistic model with granularity level, so as to recharacterize original assessment information and improve the consistency of preference matrices as far as possible. Considering the features of some large-scale group decision-making situation, where the decision makers have little opportunity to take part in multiple consensus reaching processes, hesitant fuzzy linguistic fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C$ </tex-math></inline-formula> -means clustering algorithm is developed to integrate the assessment information given by decision makers. Finally, the final decision-making results are derived. An illustrative example of assessing psychological situation of some COVID-19 infected persons clarifies the reasonability of the proposed method. Finally, we complete some comparative studies and simulation experiments to demonstrate the method's validity and advantages.
This article proposes a new network approach toward the implementation of Takagi–Sugeno (T–S) fuzzy models referred to as disjunctive fuzzy neural networks (DJFNNs). The proposed DJFNN involves a novel network architecture and a greedy learning algorithm. Being different from the existing grid-based and clustering-based network architectures, the proposed architecture adds an OR neural layer positioned between the fuzzification layer and the rule layer. In this way, the implied constraint between the number of rules and the number of fuzzy labels is excluded so that a curse of dimensionality can be overcome and more interpretable models are formed. Furthermore, inspired by the core algorithm for building a decision tree, a top–down, nonbacktracking, and greedy algorithm is proposed to learn the unknown parameters of the networks. The input space splits into smaller and smaller subspace along the predefined fuzzy grids in a supervised manner meanwhile the associated conditions of the T–S fuzzy model are identified. The greedy algorithm is applicable to high-dimensional problems since there is no exponential growth in time or space as the dimensionality increases. The new network architecture and greedy learning algorithm make the proposed DJFNN a regression model of high interpretability and good prediction capability, particularly suitable for solving the high-dimensional problems. The DJFNN was experimented with using a synthetic dataset and 28 real-world datasets and compared with classical and state-of-the-art methods through nonparametric statistical tests. The results confirmed the effectiveness of the DJFNN in terms of accuracy, interpretability, and computational cost.
